Exotic correlation spread in free-fermionic states with initial patterns

TL;DR

This paper investigates how the initial state structure in free-fermionic chains influences the velocity of correlation spreading after a quantum quench, revealing a range of velocities including zero and the Fermi velocity.

Contribution

It establishes a direct relation between initial state patterns and light-cone velocities, including cases where velocities deviate from the dispersion relation.

Findings

Correlation velocities range from zero to the Fermi velocity.

Multiple light cones can emerge depending on initial state structure.

Velocities may not always match the dispersion relation for valid momenta.

Abstract

We describe a relation between the light-cone velocities after a quantum quench and the internal structure of the initial state, in the particular case of free fermions on a chain at half filling. The considered states include short-range valence bond solids, i.e., dimerized states, and long-range states such as the rainbow. In all the considered cases the correlations spread into one or a few well-defined light cones, each of them presenting an effective velocity which can be read from the form factor. Interestingly, we find that the observed velocities range from zero to the Fermi velocity and may not always be obtained from the dispersion relation for valid momenta.